[tan(x)]'为什么等于sec^2(x)?
问题描述：
[tan(x)]'为什么等于sec^2(x)?
微分公式中有。但我想知道怎么来的。如何证明？
答
[tan(x)]'=[sin(x)/cos(x)]'
=[cos(x)*cos(x)-(-sin(x))*sin(x)]/cos^2(x)
=[cos^2(x)+sin^2(x)]/cos^2(x)
=1/cos^2(x)
=sec^2(x)